This invention claims priority to International Application No. PCT/US00/17695 filed on Jun. 28, 2000.
Geologic formations defining a reservoir for the accumulation of hydrocarbons in the subsurface of the earth contain a network of interconnected paths in which fluids are disposed that ingress or egress from the reservoir. To determine the nature and behavior of the fluids in the aforementioned network, knowledge of both the nature of the pore fluids and the porosity of the geologic formations is desired. From this information, efficient development and management of hydrocarbon reservoirs may be achieved. For example, the resistivity of geologic formations is a function of both porosity of the formations and resistivity of the fluids. Considering that hydrocarbons are electrically insulative and most formation water contains salts, resistivity measurements are a valuable tool to determine the presence of hydrocarbon reservoirs in geologic formations and to monitor the changes in hydrocarbon content as production of the hydrocarbon proceeds.
To that end, there have been many prior art attempts to determine the electrical resistivity of geologic formations surrounding and between boreholes drilled into the geologic formations of interest. In two articles, Crosshole electromagnetic tomography: A new technology for oil field characterization, The Leading Edge, March 1995, by Wilt et al. and Crosshole electromagnetic tomography: System design considerations and field results, Society of Exploration Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., measurement of geologic formation resistivity is described employing a low frequency electromagnetic (em) systems.
FIG. 1 shows the configuration of equipment used in the measurement of geologic formation resistivity between two boreholes. A transmitter, T, is located in one borehole and consists of a coil CT having multi-turn horizontal loop (vertical solenoid) of NT turns, having an effective cross section AT. The multi-turn horizontal loop carries an alternating current, IT, at a frequency of f0Hz. In free space this multi-turn horizontal loop produces a time varying magnetic field, B0. The magnetic field, B0, is proportional to the magnetic moment of the transmitter, MT, and to a geometric factor, k1. The magnetic moment of the transmitter MT is defined as follows:
MT=NTITATxe2x80x83xe2x80x83(1)
The geometric factor, k1, is a function of a spatial location and orientation of a field component of the magnetic field, B0, measured by a receiver, R, with respect to the magnetic moment of the transmitter, MT. The receiver is located spaced-apart from the transmitter, T, and typically disposed in a borehole in the earth. In free space, therefore, the magnetic field, B0, is defined as follows:
B0=k1MT.xe2x80x83xe2x80x83(2)
The receiver, R, typically includes a multi-turn loop of wire, i.e., a coil, CR, having NR turns of wire, wound about a core of high permeability metal or ferrite. The changing magnetic field BR, sensed by the receiver, R, with frequency f0, creates an induced voltage VR in the coil which is proportional to, BR; the frequency, f0; the number of turns of wire, NR; the effective cross-sectional area of the coil, AR; and the effective permeability, xcexcR, of the core of coil CR. From the foregoing, it is shown that VR is defined as follows:
VR=f0 BRNRAxcexcRxe2x80x83xe2x80x83(3)
Simplifying equation (3) above, VR may be written as follows:
VR=kRBRxe2x80x83xe2x80x83(4)
where kR=f0NRARxcexcR. The product of ARxcexcR is difficult to calculate. To accurately determine ARxcexcR, CR is calibrated in a known field, at a known frequency to find an exact value for kR. Thereafter, the magnetic field, BR sensed by the receiver, R, is related directly to the measured voltage VR by the following:
BR=VR/kRxe2x80x83xe2x80x83(5)
Such sensors measure the magnetic field in the direction of the axis of the solenoid.
When this system is placed in a conducting geologic formation the time varying magnetic field, B0, produces an electromotive force in the geologic formation, which in turn drives currents therein, shown schematically as L1. The currents, L1, are proportional to the conductivity of the geologic formation and are concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole is a result of the free space field, B0, called the primary magnetic field, and the field from the current L1, called the secondary magnetic field. The sum of these fields is a vector and the described sensors thus measure a component of the vector field in the direction of the solenoidal axis. In the examples used in the description of this invention the components of the magnetic field along the axis of the bore hole are used. In the convention used here this is defined as the z axis. Other components may be used and indeed the referenced studies indicate that other components may be used to improve the resulting determination of the distribution of resistivity in the formation.
The current L1 is typically out of phase with respect to the transmitter current It. At very low frequencies, where the inductive reactance of the surrounding formation is small, the induced current L1, is proportional to dB/dt and is consequently 90xc2x0 out of phase with respect to It. As the frequency increases, the inductive reactance increases and the phase increases to be greater than 90xc2x0.
The secondary magnetic field at the receiver, R, is caused by the induced current and consequently also has a phase shift and so the total field is complex. The total measured field has a component, BR, in-phase with the transmitter current IT, (called the real component) and a component, BI, phase shifted by 90xc2x0 (called the imaginary or quadrature component). The values of the real, BR, and quadrature components, BI, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogenous formation pierced by the drill holes. In an inhomogeneous geologic formation, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of T-R locations suffices to determine the inhomogeneous resistivity between the holes as described in the papers above.
In general, the inhomogeneous distribution of electrical resistivity is determined through a process called inversion which is well described by Audio-frequency electromagnetic tomography in 2-D, Geophysics, Vol. 58, No. 4, 1993 by Zhou et al., Electromagnetic conductivity imaging with an iterative born inversion, IEEE Transactions on Geoscience and Remote Sensing, Vol. 31, No. 4, 1993 by Alumbaugh et al., An approach to nonlinear inversion with applications to cross-well EM tomography 63rd Annual International Meeting, Society of Exploration Geophysics, Expanded Abstracts, 1993 by Torres-Verdin et al., and Crosswell electromagnetic inversion using integral and differential equations, Geophysics, Vol. 60, No. 3, 1995 by Newman. This process has been well demonstrated for the determination of resistivity in the vicinity of a single borehole or between spaced-apart boreholes wells and is described in detail by Crosswell electromagnetic tomography: System design considerations and field results, Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry, Geophysics, Vol. 60, No. 3, by Alumbaugh and Wilt, and 3D EM imaging from a single borehole; a numerical feasibility study, 1998 by Alumbaugh and Wilt.
In brief one embodiment of the inversion process consists in assigning resistivities to a multitude of cells or elements of the volume surrounding, or between, boreholes. The resistivities are systematically varied until, in a least squares sense, the results from the cellular model of the formation match the observed data taken with the field transmitter receiver system described herein. In another embodiment, a more specific model of the formation is assumed using geological, well log or other geophysical data The parameters of this model (e.g. resistivity distribution, shape, layer thickness, etc.) are varied until, again in a least squares sense, the numerical results from the model match the field results. In another embodiment direct images of the distribution of resistivity may be obtained following the principles of diffusion tomography as described by Audio-frequency electromagnetic tomography in 2-D. Geophysics, Vol. 58, No. 4, 1993 by Zhou et al. In yet another method multifrequency em data is transformed to a mathematically defined wave field domain and the data are processed following the procedures of seismic tomography. These means of interpreting the em data are included here to illustrate the fact that em methods are of practical use in determining the resistivity of geological formations.
The measurements are usually made before extraction of hydrocarbons takes place and during the extraction process. To that end, the system of FIG. 1 is principally directed to detecting hydrocarbon reservoirs and to monitoring the changes in reservoir resistivity as hydrocarbon is withdrawn in an uncased borehole. Boreholes are, however, typically cased with conductive liners (also called casings) in order to preserve the physical integrity of the borehole during subsequent hydrocarbon extraction. A problem exists in that the conductive liners are electrically conductive and are themselves inhomogenous and strongly attenuate the ac magnetic field introduced into the formation. They are very difficult and costly to remove from the borehole once installed. As a result, the system shown above in FIG. 1 does not facilitate analysis of a hydrocarbon reservoir once conductive liners are installed and extraction of the hydrocarbons begins.
The problems presented by conductive liners are described by Augustin et al., in A Theoretical Study of Surface-To-Borehole Electromagnetic Logging in Cased Holes, Geophysics Vol. 54, No. 1 (1989); Uchida et al., in Effect of A Steel Casing on Crosshole EM Measurements, SEG Annual Meeting, Texas (1991); and Wu et al. in Influence of Steel Casing on Electromagnetic Signals, Geophysics, Vol. 59, No. 3 (1994). From these papers, it is seen that the conductivity may be modeled as an additional shorted wire closely coupled to the transmitter T, shown schematically as L2 in FIG. 1.
The net or effective magnetic moment, Meff, of the transmitter, T, conductive liner combination is dictated by the inductive coupling therebetween. Physically, the resistivity of the conductive liner is very low and the inductance relatively high. This results in a current being induced in the conductive liner that is approximately 180xc2x0 out of phase of the transmitter current IT, i.e., the induced current is of opposite polarity to the transmitter current, IT, but almost of the same moment. In this manner, the magnetic field external to the conductive liner is greatly reduced. In effect, the conductive liner xe2x80x9cshieldsxe2x80x9d the transmitter, T, from the receiver, R, positioned outside of the conductive liner. The external field is produced by the difference in current, and hence moment, in the transmitter and conductive liner.
Since the induced moment in the liner is large, and nearly equal to the transmitter moment, small changes in the properties of the liner produce large fractional changes in the net of effective moment In practice, liners are known to be inhomogenous: there are variations in liner radius, thickness, permeability, and conductivity caused either by manufacturing/processing procedures or by corrosion/stress/temperature processes after installation. The central problems for the em methods described above for noncased, or open, well surveys is that the fields from the transmitter are severely attenuated in a cased well and that the net moment is highly variable as the transmitter traverses the length of the well. Without knowing the casing properties very precisely, it is difficult to distinguish between external field variations caused by the liner and the formation.
An analogous situation affects a magnetic field sensor within a cased borehole. The field to be detected induces currents concentric with the receiver coil whose sense is such as to reduce the field within the liner. The field to be detected is consequently highly attenuated and the measurement is highly influenced by the variations in attenuation caused by the variation in liner properties, an example of which is graphically demonstrated by the slope of curve 10 shown in FIG. 2. Often, the design criteria for a crosshole survey of a cased borehole reduces the signal to a level that is undetectable by standard receivers. Moreover, the variance in conductivity, permeability, and thickness along a longitudinal axis of a liner makes difficult determining the attenuation factor at any given point. This has been said to cause errors in the field measurements that are not easily corrected.
One prior art attempt to overcome this problem involved inclusion of a separate small-scale transmitter-receiver within the cased borehole to accurately measure the casing properties. The measured casing properties would then be used to correct the measured crosshole data. Lee, K. H. Kim, H. J., and Song, Yoonho, 1998. Lawrence Berkeley National Laboratory Report Number LBNL-41525.
Another prior art attempt to correct for the attenuation of a liner involved positioning of a monitor receiver adjacent to the transmitter in the cased borehole. In this manner, an attempt is made to predict the attenuation sensed by the external receiver.
A drawback with the aforementioned prior art attempts to correct for the attenuation factor concerns the implementation of auxiliary transmitters or receivers which increases the cost of a system and its complexity. Further, there is limited empirical evidence to suggest that the added cost and complexity of these systems is justified. It is not yet known whether these systems may accurately correct for the attenuation factor.
What is needed, therefore, is a cross-well measurement technique that provides accurate measurements of geologic formations without requiring detailed information concerning the properties of a liner casing the same and that is compatible with inversion methods used to interpret measurements obtained from non-cased boreholes.
Provided are a method, a computer program product and a system, to measure characteristics of geologic formations, such as hydrocarbon reservoirs, that employs modeling data to remove unwanted information from a signal carrying information concerning the geologic formation. This allows obtaining accurate information concerning the resistivity of geologic formations in which a borehole has been formed and encased with a conductive liner, such as a steel casing. Specifically, it was recognized that a magnetic field produced from a dipole transmitter within a borehole that has been cased is substantially similar to magnetic fields produced from a dipole transmitter in an uncased borehole, i.e., the spatial distribution and orientation to the two aforementioned magnetic fields are the same, only the amplitudes and phase differ. The magnetic field outside of the cased borehole is reduced in amplitude by an attenuation factor kc associated with the liner. Thus, the magnetic field produced at a point outside of the casing is a function of the product of term for the attenuation factor of the casing, kc, and a term for the response of the geologic formation, kf. Both terms are independent of the other. By factoring and removing information concerning the attenuation factor, kc, accurate measurements of the geologic formation may be determined.
To that end the invention herein includes a system having a transmitter disposed within a first area of the geologic formation and a signal generator in data communication with the transmitter. A receiver is disposed in a second area of the formation and a processor is in data communication with the receiver. With this system, a method for determining the electrical resistivity of the formation is practiced that includes producing, within a first area of the geologic formation, a first magnetic field and sensing, within a second area of the geologic formation, a second magnetic field. The second magnetic field in the second area is a function of the first magnetic field. The second area is spaced-apart from the first area The second area is surrounded with an electrically conductive casing. Associated with the casing is an attenuation factor. A signal is formed that corresponds to the second magnetic field sensed by the receiver. The signal includes information corresponding to the attenuation factor kc. A modeled magnetic field is calculated. The modeled magnetic field corresponds to the second magnetic field in an absence of the electrically conductive casing and defines a modeled representation. A quantitative value of the attenuation factor is obtained by dividing the signal by the modeled representation, and the information is removed from the signal by dividing the same with the quantitative value, thereby forming a corrected signal. The characteristics of the geologic formation are measured as a function of the corrected signal.
Alternatively, reformulating the inversion programs can explicitly solve for the casing factors at the second magnetic field positions. The key property allowing these factors to be solved is that at each second magnetic field position, the casing factor will be the same for any first magnetic field position, except for the case when the two positions are very close. Thus, the casing factor may be obtained independent of the formation factor.
Typically, a plurality of magnetic fields is sensed in the second area. This may be achieved with a single receiver disposed in the borehole formed in the second area of the geologic formation. The receiver is then moved along a longitudinal axis of the borehole. Alternatively, an array of spaced-apart receivers may be disposed in the borehole, with the receivers being spaced-apart along the aforementioned longitudinal axis. In this manner, a plurality of additional second magnetic fields is sensed. A measurement profile of the geologic formation may be generated from the plurality of additional second magnetic fields. To remove information concerning the attenuation factor, an additional signal for each of the additional second magnetic fields is formed and divided by the quantitative value. Thus, a plurality of additional corrected signals are generated and the characteristics of the geologic formation are measured as a function of both the plurality of additional corrected signals and the corrected signal.
Were an additional borehole present, e.g., formed into the first area, then a measurement profile may be obtained for differing points of the transmitter in the first area To that end, a transmitter may be sequentially located at different points along the longitudinal axis of additional borehole. Alternatively, an array of transmitters may be disposed within the borehole. At each of the aforementioned points, a plurality of additional second magnetic fields is sensed and a corresponding signal generated. In this manner, a plurality of measurement profiles are formed. The information contained in the signal concerning the attenuation factor may be removed as discussed above.
These and other embodiments of the present invention along with many of its advantages and features are described in more detail in conjunction with the text below and attached figures.